I was just reading about how Robert Byrd was famously a KKK leader in the 40's before eventually supporting civil rights by the time he died in 2010. Considering that he was born 52 years after the end of the Civil War, is there any record of him personally meeting someone who had fought in that war?
While it is documented that Senator Robert Byrd was a member of the KKK, I have not encounter any documentation specifically mentioning that he meet someone who had fought in the Civil War. It is plausible that he could have easily meet a Civil War veteran as the last veterans of the war died in the 1950's.
Pleasant Crump was the last verified confederate veteran died at the age of 104 December 31, 1951 (http://www.post-gazette.com/news/nation/2011/05/29/Last-U-S-war-veterans-Ordinary-men-in-extraordinary-times/stories/201105290242)
James Hard was the last union combat veteran died at the age of 109 on March 12, 1953 (The Chicago Tribune, March 12, 1953: http://archives.chicagotribune.com/1953/03/12/)
Lastly, Albert Woolson the last verified man to serve during the war (never was in combat) died on August 2, 1956 at the aged of 106. (St. Petersburg Times. 3 August 1956: https://news.google.com/newspapers?id=F_BRAAAAIBAJ&sjid=LHYDAAAAIBAJ&pg=7079,685655).
This is highly, highly anecdotal, but my grandmother (born in 1930s) and great-grandmother (born in 1910s) were born and raised in South Carolina and both have/had vivid memories of meeting Civil War veterans. I imagine it would have been so common as to have been a certainty that Byrd met confederate veterans.